### Abstract

We study comparator networks for selection, merging, and sorting that output the correct result with high probability, given a random input permutation. We prove tight bounds, up to constant factors, on the size and depth of probabilistic (n, k)-selection networks. In the case of (n, n/2)-selection, our result gives a somewhat surprising bound of Θ(n log log n) on the size of networks of success probability in [δ, 1 - 1/poly (n)], where δ is an arbitrarily small positive constant, thus comparing favorably with the best previously known solutions, which have size Θ(n log n). We also prove tight bounds, up to lower-order terms, on the size and depth of probabilistic merging networks of success probability in [δ, 1 - 1/poly(n)], where δ is an arbitrarily small positive constant. Finally, we describe two fairly simple probabilistic sorting networks of success probability at least 1 - 1/poly(n) and nearly logarithmic depth.

Original language | English (US) |
---|---|

Pages (from-to) | 559-582 |

Number of pages | 24 |

Journal | Theory of Computing Systems |

Volume | 30 |

Issue number | 6 |

State | Published - Nov 1997 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Theory and Mathematics
- Mathematics(all)

### Cite this

*Theory of Computing Systems*,

*30*(6), 559-582.

**On probabilistic networks for selection, merging, and sorting.** / Leighton, T.; Ma, Y.; Suel, T.

Research output: Contribution to journal › Article

*Theory of Computing Systems*, vol. 30, no. 6, pp. 559-582.

}

TY - JOUR

T1 - On probabilistic networks for selection, merging, and sorting

AU - Leighton, T.

AU - Ma, Y.

AU - Suel, T.

PY - 1997/11

Y1 - 1997/11

N2 - We study comparator networks for selection, merging, and sorting that output the correct result with high probability, given a random input permutation. We prove tight bounds, up to constant factors, on the size and depth of probabilistic (n, k)-selection networks. In the case of (n, n/2)-selection, our result gives a somewhat surprising bound of Θ(n log log n) on the size of networks of success probability in [δ, 1 - 1/poly (n)], where δ is an arbitrarily small positive constant, thus comparing favorably with the best previously known solutions, which have size Θ(n log n). We also prove tight bounds, up to lower-order terms, on the size and depth of probabilistic merging networks of success probability in [δ, 1 - 1/poly(n)], where δ is an arbitrarily small positive constant. Finally, we describe two fairly simple probabilistic sorting networks of success probability at least 1 - 1/poly(n) and nearly logarithmic depth.

AB - We study comparator networks for selection, merging, and sorting that output the correct result with high probability, given a random input permutation. We prove tight bounds, up to constant factors, on the size and depth of probabilistic (n, k)-selection networks. In the case of (n, n/2)-selection, our result gives a somewhat surprising bound of Θ(n log log n) on the size of networks of success probability in [δ, 1 - 1/poly (n)], where δ is an arbitrarily small positive constant, thus comparing favorably with the best previously known solutions, which have size Θ(n log n). We also prove tight bounds, up to lower-order terms, on the size and depth of probabilistic merging networks of success probability in [δ, 1 - 1/poly(n)], where δ is an arbitrarily small positive constant. Finally, we describe two fairly simple probabilistic sorting networks of success probability at least 1 - 1/poly(n) and nearly logarithmic depth.

UR - http://www.scopus.com/inward/record.url?scp=0031260812&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031260812&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031260812

VL - 30

SP - 559

EP - 582

JO - Theory of Computing Systems

JF - Theory of Computing Systems

SN - 1432-4350

IS - 6

ER -